/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^4 - x^3 - x^2 - 2*x + 4.

Traces:    [ -6, -2 ]
Density:   [ 0.022727273, 0.67056933 ]
Numer max: [ 4, 24 ]
Numer av:  [ 0.020144628, 1.1019284 ]
Denom max: [ 2, 32 ], [ [ <2, 1> ], [ <2, 5> ] ]
Denom LCM: [ 2, 32 ], [ [ <2, 1> ], [ <2, 5> ] ]

Character:
( 66, -66, 6, -6, 66*zeta(21)_3, -66*zeta(21)_3 - 66, 0, 2, -2, 0, 1, 
    66*zeta(21)_3 + 66, -66*zeta(21)_3, -6*zeta(21)_3, -6*zeta(21)_3 - 6, 
    6*zeta(21)_3, 6*zeta(21)_3 + 6, 0, 0, 0, 0, 0, 0, 0, zeta(21)_7^4 + 
    zeta(21)_7^2 + zeta(21)_7, -zeta(21)_7^4 - zeta(21)_7^2 - zeta(21)_7 - 1, 0,
    0, -1, 0, 0, -2*zeta(21)_3, -2*zeta(21)_3 - 2, 2*zeta(21)_3 + 2,
    2*zeta(21)_3, 0, 0, -zeta(21)_7^4 - zeta(21)_7^2 - zeta(21)_7,
    zeta(21)_7^4 + zeta(21)_7^2 + zeta(21)_7 + 1, zeta(21)_3,
    -zeta(21)_3 - 1, -zeta(21)_3*zeta(21)_7^4 - zeta(21)_3*zeta(21)_7^2
    - zeta(21)_3*zeta(21)_7 - zeta(21)_3, -zeta(21)_3*zeta(21)_7^4 -
    zeta(21)_3*zeta(21)_7^2 - zeta(21)_3*zeta(21)_7 - zeta(21)_7^4
    - zeta(21)_7^2 - zeta(21)_7, zeta(21)_3*zeta(21)_7^4
    + zeta(21)_3*zeta(21)_7^2 + zeta(21)_3*zeta(21)_7,
    zeta(21)_3*zeta(21)_7^4 + zeta(21)_3*zeta(21)_7^2 +
    zeta(21)_3*zeta(21)_7 + zeta(21)_3 + zeta(21)_7^4 + zeta(21)_7^2
    + zeta(21)_7 + 1, 0, 0, 0, 0, 0, 0, -zeta(21)_3, zeta(21)_3 + 1,
    0, 0, 0, 0, zeta(21)_3*zeta(21)_7^4 + zeta(21)_3*zeta(21)_7^2 +
    zeta(21)_3*zeta(21)_7 + zeta(21)_3, -zeta(21)_3*zeta(21)_7^4
    - zeta(21)_3*zeta(21)_7^2 - zeta(21)_3*zeta(21)_7,
    -zeta(21)_3*zeta(21)_7^4 - zeta(21)_3*zeta(21)_7^2 -
    zeta(21)_3*zeta(21)_7 - zeta(21)_3 - zeta(21)_7^4 - zeta(21)_7^2 -
    zeta(21)_7 - 1, zeta(21)_3*zeta(21)_7^4 + zeta(21)_3*zeta(21)_7^2 +
    zeta(21)_3*zeta(21)_7 + zeta(21)_7^4 + zeta(21)_7^2 + zeta(21)_7,
    0, 0, 0, 0 )
*/

G :=PermutationGroup(ATLASGroup("6M22"));
M :=
GModule(G, [
    Matrix(SparseMatrix(K, 66, 66, [
    <1, 10, 1>,  <2, 33, 1>,  <3, 5, 1>,  <4, 19, 1>,  <5, 3, 1>,  <6, 14, -1>, 
    <7, 31, 1>,  <8, 32, 1>,  <9, 25, -1>,  <10, 1, 1>,  <11, 30, 1>,  <12, 29, 
    1>,  <13, 35, -1>,  <14, 6, -1>,  <15, 16, 1>,  <16, 15, 1>,  <17, 17, -1>, 
    <18, 20, 1>,  <19, 4, 1>,  <20, 18, 1>,  <21, 26, -1>,  <22, 28, -1>,  <23, 
    23, -1>,  <24, 24, -1>,  <25, 9, -1>,  <26, 21, -1>,  <27, 34, 1/2*(-w^3 - 
    w^2 + w + 4)>,  <28, 22, -1>,  <29, 12, 1>,  <30, 11, 1>,  <31, 7, 1>,  <32,
    8, 1>,  <33, 2, 1>,  <34, 27, 1/2*(w^3 + w^2 - w - 2)>,  <35, 13, -1>,  <36,
    36, -1>,  <37, 40, 1>, <37, 55, 1/2*(w^3 + w^2 - w - 2)>, <37, 60, 1/2*(w^3 
    + w^2 - w - 2)>,  <38, 45, 1/2*(-w^3 - w^2 + w + 2)>, <38, 49, 1/2*(-w^3 - 
    w^2 + w + 4)>, <38, 52, 1/2*(-w^3 - w^2 + w + 4)>,  <39, 59, -1>,  <40, 57, 
    -1>,  <41, 39, 1/2*(w^3 + w^2 - w - 2)>, <41, 64, 1/2*(w^3 + w^2 - w - 4)>, 
    <42, 47, 1/2*(w^3 + w^2 - w - 4)>,  <43, 46, 1/2*(-w^3 - w^2 + w + 2)>, <43,
    54, 1/2*(-w^3 - w^2 + w + 4)>, <43, 65, 1/2*(-w^3 - w^2 + w + 4)>,  <44, 56,
    1/2*(w^3 + w^2 - w - 4)>, <44, 61, 1/2*(w^3 + w^2 - w - 2)>,  <45, 38, 
    1/2*(w^3 + w^2 - w - 4)>, <45, 51, 1/2*(-w^3 - w^2 + w + 2)>, <45, 62, 
    1/2*(-w^3 - w^2 + w + 2)>,  <46, 43, -1>, <46, 58, -1>,  <47, 42, 1/2*(-w^3 
    - w^2 + w + 2)>,  <48, 41, 1/2*(w^3 + w^2 - w - 2)>, <48, 50, 1/2*(w^3 + w^2
    - w - 4)>, <48, 59, -1>,  <49, 51, 1/2*(w^3 + w^2 - w - 2)>,  <50, 39, 
    1/2*(w^3 + w^2 - w - 4)>, <50, 48, 1/2*(-w^3 - w^2 + w + 2)>, <50, 64, 
    1/2*(-w^3 - w^2 + w + 2)>,  <51, 49, 1/2*(-w^3 - w^2 + w + 4)>,  <52, 51, 
    1/2*(-w^3 - w^2 + w + 4)>, <52, 62, 1>,  <53, 40, 1/2*(w^3 + w^2 - w - 2)>, 
    <53, 60, 1/2*(w^3 + w^2 - w - 4)>,  <54, 43, 1/2*(-w^3 - w^2 + w + 4)>, <54,
    58, 1/2*(-w^3 - w^2 + w + 4)>, <54, 66, 1/2*(-w^3 - w^2 + w + 4)>,  <55, 37,
    1/2*(-w^3 - w^2 + w + 4)>, <55, 53, 1/2*(w^3 + w^2 - w - 2)>,  <56, 44, -1>,
    <56, 56, 1/2*(-w^3 - w^2 + w + 2)>, <56, 61, 1/2*(-w^3 - w^2 + w + 2)>,  
    <57, 40, -1>,  <58, 46, 1/2*(w^3 + w^2 - w - 4)>, <58, 54, 1/2*(w^3 + w^2 - 
    w - 4)>, <58, 65, 1/2*(w^3 + w^2 - w - 4)>,  <59, 39, -1>,  <60, 53, 
    1/2*(-w^3 - w^2 + w + 2)>, <60, 57, 1/2*(-w^3 - w^2 + w + 4)>,  <61, 44, 1>,
    <61, 56, 1/2*(w^3 + w^2 - w - 4)>, <61, 61, 1/2*(w^3 + w^2 - w - 4)>,  <62, 
    49, 1/2*(w^3 + w^2 - w - 2)>, <62, 52, 1>,  <63, 42, 1/2*(w^3 + w^2 - w - 
    2)>, <63, 47, -1>, <63, 63, -1>,  <64, 41, 1/2*(-w^3 - w^2 + w + 2)>, <64, 
    59, 1/2*(-w^3 - w^2 + w + 4)>,  <65, 43, 1/2*(w^3 + w^2 - w - 2)>, <65, 66, 
    1/2*(w^3 + w^2 - w - 4)>,  <66, 46, 1>, <66, 54, 1/2*(w^3 + w^2 - w - 2)> 
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]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [4, -2, -1, -1, 1])> where K is 
RationalField();
K<w> := BaseRing(M);
K;
M;
